Phone is almost completely unresponsive. Please Help!

I left my phone in my car overnight last night. This was in NY and it was probably 25F outside. When I retrieved my phone in the morning, the phone was dead and very cold. I tried to turn it on, and nothing. I figured either the battery was dead or the cold was messing with the phone. So I plugged it into my charger and waited a bit. Hit the power button and still, nothing! Plugged in it for another two hours and still nothing.

What I haven't tried:
-I wanted to try another battery, but unfortunately don't have one available to test. At this point, I do not think it is the battery, however cannot be sure.

What I've noticed:
-When the phone is plugged in, nothing happens. No LED indicators blinking, no charging screen, etc.
-The only time I get action from the phone is when I insert the battery. When I do, the phone vibrates, I see the black samsung galaxy s4 screen for probably 1.5 seconds then it goes blank (aka the screen turns off). I can reproduce this by pulling the battery and putting it back in. But once the screen goes blank, the phone is totally unresponsive.
-Over the past few days, I noticed some weird behavior with the power button not turning off the screen with a quick tap. I spoke to Samsung and they confirmed the phone shouldn't auto-turn-on once I insert a battery. I dissembled the phone and made sure the power button wasn't stuck or malfunctioning. All seems fine.

Potential issues:
-The way I see it, the problem could be due to a dead battery or a battery that cannot charge because of a bad USB jack on the phone. I'd love to be able to isolate one of the issues before ordering the needed parts.

Does anybody else have any ideas or things I can try? Please help. I am out of ideas and desperately would like to get my phone back up and running.

Extremely cold phone brought into a warm and likely more humid environment will cause condensation. Plugging that device into power before letting it warm up and dry will very likely cause a short circuit. I would say it is likely fried. Next time put the phone in a bowl of uncooked rice before bringing it inside and if possible putting it in a warm dry place first till it is room temp to the touch before attempting to power it ON.

It may be too late, but pull the battery and leave the phone and the battery alone for 24 hours. (If you can, now is the time for the "rice trick" - put the phone and battery in a bag or jar of uncooked white (not instant) rice while they sit - the warmer air inside is going to cause condensation, and the rice will absorb a lot of that. If you have a pound or two of silica gel, even better.)

After 24 hours, put the battery back in the phone and see if it turns on. If it does, turn it off, plug in the charger and leave it alone (still in the rice) for another 24 hours.)

After that it should be back to normal, although the battery may have lost a few months of life. Charging a lithium battery when it's below freezing (32F) is bad for it. You can discharge the battery at down to -4F, but that will reduce the life a little bit.

The screen is another matter. An LCD screen normally shouldn't be allowed to reach a temperature lower than -4F. (Depending on the "liquid" part of "liquid crystal", the liquid can freeze and the crystals can puncture the film, destroying the screen.) Operating down at 25F? It may not look great, but it shouldn't cause damage. (The screen will lag when it's cold, and lag pretty badly when it's very cold.)

BTW, "insert the battery. When I do, the phone vibrates, I see the black samsung galaxy s4 screen for probably 1.5 seconds then it goes blank" usually means a wet phone. It's probably too late, but you could try alcohol. Oh, no! My Phone got Wet!

The rule of thumb is that if the temperature is too low or too high for you to be comfortable in a short sleeved shirt, it's too low or too high for the phone.

There are two reasons to not leave a phone in a car. 1) Temperature - the 150F or more in a car parked in the sun in the summer (yes, in NY - I grew up in NYC and raised many blisters as a kid touching the railing on the boardwalk in the summer) can destroy both the phone and the battery, it's not just the winter that's a problem, and 2) the very real possibility of coming back to a car with a broken window and no cellphone. Look on eBay - you'll see a lot of "bad IMEI" or "bad ESN" phones for sale. That doesn't mean the IMEI or ESN "broke", it means that the owner reported the phone stolen.